We investigate the entrainment, deposition and motion of coarse spherical particles within a turbulent shallow water stream down a steep slope. This is an idealization of bed-load transport in mountain streams. Earlier investigations have described this kind of sediment transport using empirical correlations or concepts borrowed from continuum mechanics. The intermittent character of particle transport at low-water discharges led us to consider it as a random process. Sediment transport in this regime results from the imbalance between entrainment and deposition of particles rather than from momentum balance between water and particles. We develop a birth-death immigration-emigration Markov process to describe the particle exchanges between the bed and the water stream. A key feature of the model is its long autocorrelation times and wide, frequent fluctuations in the solid discharge, a phenomenon never previously explained despite its ubiquity in both nature and laboratory experiments. We present experimental data obtained using a nearly two-dimensional channel and glass beads as a substitute for sediment. Entrainment, trajectories, and deposition were monitored using a high-speed digital camera. The empirical probability distributions of the solid discharge and deposition frequency were properly described by the theoretical model. Experiments confirmed the existence of wide and frequent fluctuations of the solid discharge, and revealed the existence of long autocorrelation time, but theory overestimates the autocorrelation times by a factor of around three. Particle velocity was weakly dependent on the fluid velocity contrary to the predictions of the theoretical model, which performs well when a single particle is moving. For our experiments, the dependence of the solid discharge on the fluid velocity is entirely controlled by the number of moving particles rather than by their velocity. We also noted significant changes in the behaviour of particle transport when the bed slope or the water discharge was increased. The more vigorous the stream was, the more continuous the solid discharge became. Moreover, although 90 % of the energy supplied by gravity to the stream is dissipated by turbulence for slopes lower than 10 %, particles dissipate more and more energy when the bed slope is increased, but surprisingly, the dissipation rate is nearly independent of fluid velocity. A movie is available with the online version of the paper.

A longstanding problem in the study of sediment transport in gravel-bed rivers is related to the physical mechanisms governing bed resistance and particle motion. To study this problem, we investigated the motion of coarse spherical glass beads entrained by a steady shallow turbulent water flow down a steep twodimensional channel with a mobile bed. This experimental facility is the simplest representation of sediment transport on the laboratory scale, with the tremendous advantages that boundary conditions are perfectly controlled and a wealth of information can be obtained using imaging techniques. Flows were filmed from the side by a high-speed camera. Using image processing software made it possible to determine the flow characteristics such as particle trajectories, their state of motion ͑rest, rolling, or saltating motion͒, and flow depth. In accordance with earlier investigations, we observed that over short time periods, sediment transport appeared as a very intermittent process. To interpret these results, we revisited Einstein's theory on sediment and derived the statistical properties ͑probability distribution and autocorrelation function͒ of the key variables such as the solid discharge and the number of moving particles. Analyzing the autocorrelation functions and the probability distributions of our measurements revealed the existence of long-range correlations. For instance, whereas theory predicts a Binomial distribution for the number of moving particles, experiments demonstrated that a negative binomial distribution best fit our data, which emphasized the crucial role played by wide fluctuations. These frequent wide fluctuations stemmed particle entrainment and motion being collective phenomena rather than individual processes, contrary to what is assumed in most theoretical models.

Large Scale Particle Image Velocimetry (LS-PIV) is used to measure the surface flow velocities in a mountain stream during high flow conditions due to a reservoir release. A complete installation including video acquisition from a mobile elevated viewpoint and artificial flow seeding has been developed and implemented. The LS-PIV method was adapted in order to take into account the specific constraints of these high flow conditions. Using a usual LS-PIV data processing, significant variations of the water surface elevation were taken into consideration in the image rectification. An intensity threshold was applied to focus on artificial tracers without considering stationary waves and sun reflections on the flow surface. A site-specific float coefficient of 0.79 based on measured vertical velocity profiles was used to convert surface velocities into depth-averaged velocities. Comparison between LS-PIV assessments and 2Dh numerical calculations with the code Rubar20 allows verification and extrapolation of LS-PIV data. LS-PIV velocity measurements permit to assess discharges over the whole high flow event in agreement with leaded current-meter measurements performed at a downstream bridge

Abstract. Since the turn of the 21st century, image-based velocimetry techniques have become an increasingly popular approach for determining open-channel flow in a range of hydrological settings across Europe and beyond. Simultaneously, a range of large-scale image velocimetry algorithms have been developed that are equipped with differing image pre-processing and analytical capabilities. Yet in operational hydrometry, these techniques are utilised by few competent authorities. Therefore, imagery collected for image velocimetry analysis (along with reference data) is required both to enable inter-comparisons between these differing approaches and to test their overall efficacy. Through benchmarking exercises, it will be possible to assess which approaches are best suited for a range of fluvial settings, and to focus future software developments. Here we collate and describe datasets acquired from seven countries across Europe and North America, consisting of videos that have been subjected to a range of pre-processing and image velocimetry analyses (Perks et al., 2020, https://doi.org/10.4121/uuid:014d56f7-06dd-49ad-a48c-2282ab10428e). Reference data are available for 12 of the 13 case studies presented, enabling these data to be used for reference and accuracy assessment.

Abstract. In this note we are interested in the modelling of sediment transport phenomena. We mostly focus on bedload transport and we do not consider suspension sediment processes. We first propose a numerical scheme for the classical Saint-Venant -Exner model. It is based on a relaxation approach for the whole system and it works with all sediment flux function. The stability of the scheme is investigated and some numerical tests are proposed. We exhibit that this coupled approach is more stable than the splitting approach that is mostly used in industrial softwares. Then we derive an original three layers model in order to overcome the difficulties that are encountered when using the classical Exner approach and we present a related relaxation model.

Steep streams with massive sediment supply are among the most complex systems to study, even in the laboratory. Their shallow sediment‐laden flows create self‐adjusting bed geometries that evolve rapidly. Often, morphological changes and flow processes cannot be dissociated. Because these very shallow and unstable flows cannot be equipped with measurement sensors, image analysis techniques, such as photogrammetry (e.g., structure‐from‐motion, SfM) and large‐scale particle image velocimetry (LSPIV), are interesting options for capturing the characteristics of these systems. The present work describes a complete procedure using both techniques to measure spatially distributed surface velocity and bed properties (deposit patterns, channel slope, and local roughness). The velocity data are used to assess the local flow directions along which the channel slope and roughness are extracted from the SfM digital elevation models. Fergusons “variable power equation” friction law, having been previously validated by comparison with approximately 100 local flow depth measurements, was used in a second step with the collected data to reconstruct a complete mapping of the depth‐averaged flows, thereby enabling a comprehensive analysis of the hydrogeomorphic system where shallow water equations apply. The assumptions, details, use of the friction law with roughness standard deviation rather than diameter as parameter and limitations of the procedure as well as possible sources of errors are discussed here, along with possibilities for improvements. This affordable and simple‐to‐implement procedure can provide a large amount of data, allowing for a more comprehensive analysis of complex hydraulic systems.

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